1. Field of the Invention
The present invention relates to communications systems and, more particularly, to digital signal decoders.
2. Description of the Related Technology
Most electronic communication systems in use today include a transmitter to transmit an electromagnetic signal and a receiver to receive the transmitted signal. The transmitted signal is typically corrupted by noise and, therefore, the receiver must operate with received data that reflects the combination of the transmitted signal and noise. Thus, the receiver receives data y(t) at a time t, where y(t)=s(t)+n(t), the sum of the transmitted signal and additive noise. The received data equation can be expanded as follows: ##EQU1## where A(t) is the signal amplitude, .omega..sub.o is the carrier or reference frequency, .theta. (t) is the time-varying phase function and n (t) is noise.
Many of these communication systems require that the receiver demodulate information in the received signal which depends on proper demodulation of the signal phase angle at all times during transmission. The demodulation of the signal phase angle is problematic in view of the pervasiveness of noise. Therefore, for this class of receivers it is desirable to optimize phase demodulation, which is equivalent to optimizing an estimation of the phase function .theta. (t).
Digital communication involves modulation that changes discontinuously in accordance with a transmitted coded signal, e.g., discontinuous phase shifts of a sequence of short-duration sinusoids (chip waveforms), as in quadrature phase shift keying (QPSK). Each coded signal represents a transmitted quantization level or symbol. One example type of coded signal is a maximum length binary sequence (W. W. Peterson, Error-Correcting Codes, MIT Press, Cambridge, Mass., 1961). Such a coded signal is a binary stream which is generated by a decorrelated cyclic shift, i.e., each coded signal is designed to be uncorrelated with any another. Coded signal transmission is used today in many communications domains including, for example, digital cellular telephone systems.
Uncompensated multipath, synchronization errors, and phase disparity between transmitter and receiver cause a received code to have phase values that are different from those of the transmitted code, even without additive noise. The differences between received and transmitted phase samples can be modeled as random perturbations that are correlated from sample to sample. A conventional maximum likelihood (correlation) receiver does not account for such noise-free randomness; received noise-free samples are assumed to have the same phase values as the transmission for correlation processing. Thus, a need exists for an optimum receiver/demodulator for digital transmission in the presence of such errors.
The maximum a posteriori (MAP) estimator uses each phase value in a hypothesized coded signal as an element of the prior mean phase vector .theta..sub.m. For the same data, different MAP phase estimates are obtained for different hypothesized signals. The set of MAP phase estimates corresponding to a given hypothesized coded signal determines a reference signal for correlation with the original data.
The resulting receiver performs better than a conventional maximum likelihood processor for phase perturbed signals, but a different .theta..sub.m vector and associated MAP phase estimate is needed for each coded signal hypothesis. For many coded signal hypotheses, receiver complexity for MAP estimator-correlator processing seems to be prohibitive. Thus, a need exists for a simple implementation of a MAP estimator-correlator receiver for digital communications.